28-07-2021 Answers

1. Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days?

Answer: 20

Solution: Let the initial amount of grass be g and growth rate per day be r.

The amount which a cow eats in one day = c.

g + 24r = 24*70*c - Eqn1

g + 60r = 30*60*c - Eqn2

Using the above two equations, 36r=120c - Eqn3,

Now for 96 days, let the days required be n.

g + 96r = 96 * n * c - Eqn4,

Subtracting Eqn2 from Eqn4,

36r = c(96n-1800), Now from Eqn3, 36r=120c.

Hence 120c=c(96n-1800), solving n= 1920/96 = 20

2. If the list price of a book is reduced by Rs.5, then a person can buy 5 more books for Rs. 300. The list price of the book is

Answer: Rs.20

Solution: Let the list price be x. Number of books that can be bought = 300/x

Now when reduced by Rs.5, number of books that can be bought = 300/(x-5).

Hence 300/(x-5)  - 300/x = 5,

300x - 300x + 1500 = 5 * x * (x-5),

x^2 -5x -300 = 0,

(x-20)(x+15) = 0.

Solving x=20 (as the price cannot be negative for x=-15.

3. In a party all the Indian guests ate 2 dosas, each Russian guest ate 4, each Belgian ate 8, and all Chinese guests ate 12. There had been a total of 468 dosas served. The number of guests from each country was equal. How many guests in total were in the party?

Answer: 72

Solution: Let the number of guest from each country be x.

2x+4x+8x+12x=468, x=468/26=18.

Total num of guests = 4x = 4*18 = 72.

4. Lavanya has the same number of sisters as she has brothers, but her brother Ram has twice as many sisters as he has brothers. How many children are there in the family?

Answer: 7

Solution: Let num of male children be b and female children be s.

b=s-1,

2(b-1)=s.

Using the eqns, b+1=2b-2, b=3 and s=4

Total children=3+4=7

5. A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day? 

Answer: 8

Solution: He ate 8 bananas on the first day.

Let the bananas he ate on first day be x.

In five days,  x + (x+6) + (x+12) + (x+18) + (x+24) = 5x + 60

Now 5x+60 = 100, hence x=8.

6. In a car wheel, two spokes cover 15 degree. Then for an entire car, how many spokes are there?

Answer: 96

Solution: Number of spokes in a single wheel= 360/15 = 24

A car has to have minimum four wheels. Hence total number of spokes = 24*4 = 96 or should be higher. Among the given options 96 is the answer

7. An investor purchased shares of stock at a certain price. If the stock increased in price at Rs 0.25 per share and the total increase in the value for the shares purchased was Rs 12.50, how many shares did the investor purchase?

Answer: 50

Solution: Num of stocks purchased = 12.50/0.25 = 50

8. M men agree to purchase a gift for Rs. D each contributing equal amount. If three men drop out how much more will each have to contribute towards the purchase of the gift?

Answer: 3D/(M*M - 3M)

Solution: Original contribution by one man = D/M.

Now as three left, additional contribution = 3D/M/(M-3) = 3D/(M*M - 3M)

9. The price of a table is Rs. 400 more than the price of a chair.If 6 tables and 6 chairs together cost Rs.4800, what is the price of a table?

Answer: Rs.600

Solution: Let price of a chair be x, price of table=x+400.

6(x+x+400)=4800, Solving x=200,

Price of table = x+400 = Rs.600

10. Three members went for hunting in a forest with equal number of cartridges. While crossing a river, the cartridges of two of them got wet and hence discarded. Then the third person divided his cartridges equally. After 4 shots by each person, total cartridges remaining were equal to the cartridges the third person shared. How many total cartridges were there initially when they started hunting?

Answer: 54

Solution: Let initial num be 9x and hence each had 3x.

Now third person shared x,x,x

As they fired four shots,

3(x-4) = x,

Solving x = 6

Total cartridges = 9x = 54

11. Two full tanks one shaped like a cylinder and the other like a cone contain liquid fuel. The cylindrical tank held 500 liters more then the conical tank.  After 200 liters of fuel is pumped out from each tank the cylindrical tank now contains twice the amount of fuel in the conical tank. How many liters of fuel did the cylindrical tank have when it was full?

Answer: 1200 liters

Solution: Let fuel in cylindrical tank be x litres and in conical be y litres.

x = y+500 - Eqn 1

Also it is given x-200 = 2(y-200)

Using eqn 1, y+500-200 = 2y-400, y=700.

Hence cylindrical tank had y+500 = 1200 liters.

12. The dimensions of a certain machine are 48" X 30" X 52". If the size of the machine is increased proportionately until the sum of its dimensions equals 156", what will be the increase in the shortest side?

Answer: 6"

Solution: Let the factor for proportional increase = a.

48a + 30a + 52a = 156,

a = 156/130.

Hence shortest side will become = 30*156/130 = 36"

Hence increase = 36-30 = 6"

13. Y catches 5 times more fish than X. If total number of fish caught by X and Y is 42, what is the number of fish caught by Y?

Answer: 35

Solution: Let number caught by X = a. Then number caught by Y = 5a.

a+5a = 42,  a=7. 

Number caught by Y = 5a = 35.

14. A physical education teacher arranges students and finds that the number of rows and columns are equal. He finds that 20 more students have come additionally and he could place them to completely fill yet another row (or column). What is the final number of the students who have been arranged?

Answer: 420

Solution: As the initial number of rows and columns are equal, the arrangement is square shaped. Now when 20 arrive if they can completely fill one row or column it means earlier 20 were in a row or column. Hence total number of students = 20 *20 + 20 (who arrived additionally) = 420.

15. Sandhya wanted to buy 5 kgs of oranges. The vendor kept the 5 kg weight on the right side and weighed 6 oranges for that. She doubted on the correctness of the balance and placed 5 kg weight on the left side and she could weigh 20 oranges for 5 kgs. If the balance was accurate how many oranges she would have got for 10 kilograms?

Answer: 26

Solution: Let the additional weight on the left side be x.

Let the average weight of an orange be a.

x+6a = 5kgs

x+5 = 20a

Solving, a=5/13 kgs.

Hence for 10 kgs she should have got 10/1/5/13 = 26 oranges.

16. If  S= (10/7 * (R+2W)) +  QP, which of the following is true?

Answer: P=(7S-10R-20W)/7Q

Solution: The above eqn becomes,

7S = 10R + 20W + 7QP.

So P=(7S-10R-20W)/7Q

17. A quiz has 50 questions. A person scores 1 mark for a correct answer, –1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a person is 32, the number of questions answered wrongly by that person cannot be less than

Answer: 3

Solution: Let number of correctly answered be c, wrongly answered be w and not attempted be u.

c - w/3 -u/6 = 32,

6c -2w - u = 192 - Eqn 1

c + w + u = 50   - Eqn 2

Adding both Eqn1 and 2,

7c - w = 242,

c = (242+w)/7.

c should be a whole number. Hence for 242+w to be divisible by 7, minimum required value of w is 3 (as 245 is divisible by 7).

Hence answer is 3.

18. A servant is paid Rs.100 plus one shirt for a full year of work. He works for 6 months and gets Rs.20 plus a shirt. What is the cost of the shirt?

Answer: Rs 60

Solution: In 6 months he is supposed to get Rs.50 + Half shirt.

But he got Rs.20 and a full shirt.

Let the cost of the shirt be x.

50 + x/2 = 20 + x,

x = 60

19. If G(0) = -1,  G(1)= 1 and G(N) = G(N-1) – G(N-2) then what is the value of G(6)?

Answer: -1

Solution: As G(N) = G(N-1) – G(N-2),

G(2) = G(1) - G(0) = 1 - (-1) = 2

G(3) = 2-1 = 1

G(4) = 1-2 = -1

G(5) = -1-1 = -2

G(6) = -2 -(-1) = -1

20. From its total income, a sales company spent Rs.20,000 for advertising, half of the remainder on commissions and had Rs.6000 left. What was its total income?

Answer: Rs.32000

Solution: Let total income = x

(x-20000) - 1/2(x-20000) = 6000

x/2 -10000 = 6000

Solving x=32000

21. Ajay, Bimal, Chandok, David play a game. In the beginning all had equal points (score). The winner collects half the amount of all other players. In the first round Chandok wins. In the 2nd round Bimal wins and in the 3rd round Bimal again wins. At this time, the scores of Ajay,Bimal,Chandok are : Ajay=50, Bimal=1250, Chandok=250. What was the score of David in the beginning of the game?

Answer: 400

Solution: As A and D did not win, both will have same points (Score). So total points at the end of 3rd round = 50+1250+250+50=1600.

As every one had equal score in the beginning, score of David in the beginning of the game = 1600/4 = 400.

22. If .2t = 2.2 - .6s and .5s = .2t + 1.1, then what is the value of s?

Answer: 3

Solution: Using the eqns given,

.5s = 2.2 - .6s + 1.1

s = 3.3/1.1 = 3

23. In a zoo, there are deers and ducks. If the heads are counted, there are 62 heads, while the number of legs is 202. What is the number of deers in the zoo?

Answer: 39

Solution: Let number of deers be D and ducks be U.

D+U = 62 - Eqn 1

4D+2U = 202 - Eqn 2

Solving these two eqns, D=39

24. Janani took a test that had 20 questions.  The total score was computed by awarding 10 points for each correct answer and deducting 5 points for each incorrect answer.  Janani answered all 20 questions and received a score of 125.  How many of the questions were answered incorrectly?

Answer: 5

Solution: Let the num of questions answered correctly be x. Then answered wrongly=20-x.

10x - (20-x)*5 = 125, solving x=225/15 = 15.

Hence questions answered incorrectly = 20-15 = 5

25. 5 coffee and 4 tea costs Rs.96. 5 badam milk and 6 coffee costs Rs.32 and 7 tea and 6 badam milk costs Rs.37. What is the combined price of 1tea, 1 coffee and 1 badam milk?

Answer: Rs.15

Solution: Let the price of one coffee, tea and badam be c,t,b.

5c+4t=96

5b+6c=32

7t+6b=37

Adding all eqns, 11c+11b+11t = 165

Hence c+b+t = 15